Overloading applies to objects, not operators. (In Perl 6 you can override operators and/or write your own.) If you want to know if an object is overloading, use overload::Overloaded( $obj ). If you want to know if it's overloading eq in particular, you can check overload::Method( $obj, 'eq' ), but you'll also have to look for stringification (overload::Method( $obj, q{""} )).

...how should I understand it?

Just that eq forces its operands to be strings in order to do its job. A regular expression stringifies as you've found (it's a blessed reference to an undef with regex magic added).

You might also be interested in overload::StrVal( $obj ), which gives you the string value of $obj without string overloading. For a regular expression, this is similar to "Regexp=SCALAR(0x1d10860)".